Tatuada is the feminine past participle of the verb tatuar, meaning "to tattoo". It's a visually striking word that you don't often find in sentimental ballads.
In the song, the line "Que mi alma fue tatuada en tu piel" translates to "That my soul was tattooed on your skin". This is a beautiful and modern metaphor for a love that is so deep and permanent that it has left an indelible mark, making the connection between the two people unforgettable.
This song is a powerful, emotional plea from someone who knows a relationship is over. The singers aren't fighting; instead, they're asking their former lover how to be remembered. They want to be recalled not in anger or sadness, but for the best parts of their time together. They ask their ex to think of them "Recuérdame amándote" (Remember me loving you) and "Mirándote a los ojos" (Looking into your eyes).
It's a song about a breakup that accepts the coming pain, mentioning when "el frío y la tristeza / Se funden y te abrazan" (the cold and sadness / Merge and embrace you). But even with that sadness, the core request is to remember the love as something permanent and beautiful. The final line is unforgettable: "Que mi alma fue tatuada en tu piel" (That my soul was tattooed on your skin), suggesting a love so deep it leaves a mark that can never be erased.